The discussion revolves around finding the general solution to a second-order linear homogeneous differential equation, specifically y'' - 5y' + 6y = 0.
The discussion includes various interpretations of the factorization process, with some participants questioning the accuracy of previous attempts. There is a suggestion to check the validity of the proposed solutions, indicating a productive direction in the exploration of the problem.
Some participants express uncertainty about the factorization of the characteristic equation, leading to differing proposed solutions. There is a lack of consensus on the correct approach to the problem.
Your factorization is incorrect. (m - 1)(m - 5) = m2 - 6m + 5, not m2 - 5m + 6.JosephK said:Homework Statement
1. Find the general solution to the differential equation:
y''-5y'+6y = 0
Homework Equations
The Attempt at a Solution
m^2 - 5m + 6 = 0
(m-1)(m-5) = 0
JosephK said:y' = Ae^x+Be^5x
(m - 3)(m - 2) ?JosephK said:This cannot be factored.